There is some information on FreeREG for this family, and also some trees on line. Some trees have John's father as William Keep with mother Isabella Etton, but you would need to check this out as quite often on line trees can have incorrect information in them. FreeREG has a John marrying an Elizabeth ? 16/11/1574 so could be the son-this is Wantage. Alice was baptised 3/5/1548 Wantage, Annis Keepe was baptised 16/9/1550-there is an Annis Keepe marrying a John Pratt 1/7/1593, but I believe that you have your Annis as dying in that year. There is also a Jhone Keepe with parents John and Alice baptised 6/1/1540 so she would have been the first born, and they may well have married round about 1539 at a guess.
regards.